Data Fitting with Signomial Programming Compatible Difference of Convex Functions

TL;DR

This paper introduces a new SDMA function class for fitting signomial models to data, enhancing modeling flexibility in Signomial Programming and demonstrating high-accuracy fits in engineering applications.

Contribution

It proposes a novel SDMA function class that leverages DC functions for improved signomial data fitting within SP frameworks.

Findings

RMS error reduced to less than 1% in all examples

Demonstrated effective fitting in 2D, 3D, and airfoil data

Enhanced modeling flexibility for engineering optimization

Abstract

Signomial Programming (SP) has proven to be a powerful tool for engineering design optimization, striking a balance between the computational efficiency of Geometric Programming (GP) and the extensibility of more general optimization methods like Sequential Quadratic Programming (SQP). But when an existing engineering analysis tool is incompatible with the mathematics of the SP formulation, options are limited. Previous literature has suggested schemes for fitting GP compatible models to pre-computed data, but no methods have yet been proposed that take advantage of the increased modeling flexibility available in SP. This paper describes a new Soft Difference of Max Affine (SDMA) function class that is constructed from existing methods of GP compatible fitting and the theory of Difference of Convex (DC) functions. When a SDMA function is fit to data in log-log transformed space, it becomes either a signomial or a set of signomials upon inverse transformation. Three examples of fitting are presented here, including simple test cases in 2D and 3D, and a fit to the performance data of the NACA 24xx family of airfoils. In each case, RMS error is driven to less than 1%.